1 Find the directional derivative of f (x, y, z) = 2z?x + y° at the point (2, 1, 2) in the direction of the vector -i+ (Use symbolic notation and fractions where needed.) directional derivative:
1 Find the directional derivative of f (x, y, z) = 2z?x + y° at the point (2, 1, 2) in the direction of the vector -i+ (Use symbolic notation and fractions where needed.) directional derivative:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Directional Derivative Calculation**
Find the directional derivative of the function
\[ f(x, y, z) = 2z^2x + y^3 \]
at the point \((2, 1, 2)\) in the direction of the vector
\[
\frac{1}{\sqrt{5}} \mathbf{i} + \frac{2}{\sqrt{5}} \mathbf{j}.
\]
(Use symbolic notation and fractions where needed.)
**Directional Derivative:** \[ \boxed{\phantom{fill in}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51ff2e68-0bd1-44c4-8696-122fa89f1551%2Fd7b2b419-30c5-4005-a3ee-1ba2d848a2d2%2Ff0e2gwj_processed.png&w=3840&q=75)
Transcribed Image Text:**Directional Derivative Calculation**
Find the directional derivative of the function
\[ f(x, y, z) = 2z^2x + y^3 \]
at the point \((2, 1, 2)\) in the direction of the vector
\[
\frac{1}{\sqrt{5}} \mathbf{i} + \frac{2}{\sqrt{5}} \mathbf{j}.
\]
(Use symbolic notation and fractions where needed.)
**Directional Derivative:** \[ \boxed{\phantom{fill in}} \]
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